16楼: Originally posted by 天上行杯 at 2017-04-20 07:41:26
不好意思，打错了，"特征值"改为"特征根"，也改动"X1+……+Xn=C对角线元素和≤1"为"…………≤n"

12楼: Originally posted by yfg0525 at 2017-04-19 21:03:51
大致思路：
1. 问题等价于证明 |E+C|<=2^n, for any C 为正交矩阵；
2.注意到|E+C^T|=|E+C|,于是|E+C|=|(E+C^T)(E+C)|^1/2=|2E+C+C^T|^1/2;
3.利用性质 A正定等价于A可以写成 B*B^T的性质，我们知道(E+C^T)(E ...

11楼: Originally posted by fungarwai at 2017-04-18 19:25:53
det(A+B)=det(A)det(E+A^T B),det(A)=\pm 1

正交矩阵的特征值模等于1
A^T B是正交矩阵，可对角化,设A^T B=PDP^{-1},D=diag(\lambda_1,\lambda_2,...,\lambda_n)
det(E+A^T B)=det(P^{-1})det(E+D)det(P)=det(E ...

11楼: Originally posted by fungarwai at 2017-04-18 19:25:53
det(A+B)=det(A)det(E+A^T B),det(A)=\pm 1

正交矩阵的特征值模等于1
A^T B是正交矩阵，可对角化,设A^T B=PDP^{-1},D=diag(\lambda_1,\lambda_2,...,\lambda_n)
det(E+A^T B)=det(P^{-1})det(E+D)det(P)=det(E ...